The special orthogonal group \(SO(3)=\lbrace R \in \mathbb {R}^{3\times 3} \mid RR^T = \mathrm {I}_{3\times 3}, \det R = 1 \rbrace \)  is a compact Lie group that contains the 3-by-3 orthogonal matrices with determinant one, i.e., all rotation matrices [1]}.
Associated with \(SO(3)\)  is the Lie algebra \(so(3)\) , consisting of the set of skew-symmetric 3-by-3 matrices.
